Paper:

# Parallel Learning Model and Topological Measurement for Self-Organizing Maps

## Michiharu Maeda^{*}, Hiromi Miyajima^{**}, and Noritaka Shigei^{**}

^{*}Department of Control and Information Systems Engineering, Kurume National College of Technology, 1-1-1 Komorino, Kurume 830-8555, Japan

^{**}Department of Electrical and Electronic Engineering, Faculty of Engineering, Kagoshima University, 1-21-40 Korimoto, Kagoshima 890-0065, Japan

*J. Adv. Comput. Intell. Intell. Inform.*, Vol.11 No.3, pp. 327-334, 2007.

- [1] T. Geszti, “Physical models of neural networks,” World Scientific, 1990.
- [2] J. Hertz, A. Krogh, and R. G. Palmer, “Introduction to the theory of neural computation,” Addison-Wesley, 1991.
- [3] T. Kohonen, “Self-organization and associative memory,” Springer-Verlag Berlin, 1989.
- [4] T. Kohonen, “The self-organizing map,” Proc. IEEE, Vol.78, pp. 1464-1480, 1990.
- [5] T. Kohonen, “Self-organizing maps,” Springer-Verlag Berlin, 1995.
- [6] H.-U. Bauer and K. R. Pawelzik, “Quantifying the neighborhood preservation of self-organizing feature maps,” IEEE Trans. Neural Networks, Vol.3, pp. 570-579, 1992.
- [7] T. Martinetz and K. Schulten, “Topology representing networks,” Neural Networks, Vol.7, pp. 507-522, 1994.
- [8] M. Maeda, H. Miyajima, and S. Murashima, “Parallel processing for self-organization,” IEICE Proc. 7-th Circuits & Syst. Karuizawa Workshop, pp. 139-143, 1994.
- [9] M. Maeda, H. Miyajima, and S. Murashima, “Parallel-sequential self-organizing algorithms for feature maps,” IEICE Proc. Symp. Nonlinear Theory and its Applications, pp. 275-278, 1994.
- [10] T. Villmann, M. Herrmann, and T. M. Martinetz, “Topology preservation in self-organizing feature maps: Exact definition and measurement,” IEEE Trans. Neural Networks, Vol.8, pp. 256-266, 1997.
- [11] M. Maeda and H. Miyajima, “Parallel manner for self-organizing maps and its topology preservation,” IEICE Technical Report, Vol.NLP99-129, pp. 41-48, 2000.
- [12] M. Maeda, H. Miyajima, and N. Shigei, “A model of parallel learning in self-organizing maps and topological measurement,” Proc. Int. Conf. Intelligent Technologies, pp. 133-140, 2005.
- [13] T. Kohonen, “Analysis of a simple self-organizing process,” Biol. Cybern., Vol.44, pp. 135-140, 1982.
- [14] R. Durbin and D. Willshaw, “An analogue approach to the traveling salesman problem using an elastic net method,” Nature, Vol.326, pp. 689-691, 1987.
- [15] B. Angéniol, G. de La C. Vaubois, and J.-Y. Le Texier, “Selforganizing feature maps and the traveling salesman problem,” Neural Networks, Vol.1, pp. 289-293, 1988.
- [16] H. Ritter and K. Schulten, “On the stationary state of Kohonen’s self-organizing sensory mapping,” Biol. Cybern., Vol.54, pp. 99-106, 1986.
- [17] H. Ritter and K. Schulten, “Convergence properties of Kohonen’s topology conserving maps, Fluctuations, stability, and dimension selection,” Biol. Cybern., Vol.60, pp. 59-71, 1988.
- [18] T. M. Martinetz, S. G. Berkovich, and K. J. Schulten, “ “Neuralgas” network for vector quantization and its application to timeseries prediction,” IEEE Trans. Neural Networks, Vol.4, pp. 558-569, 1993.
- [19] M. Maeda and H. Miyajima, “Competitive learning methods with refractory and creative approaches,” IEICE Trans. Fundamental, Vol.E82-A, pp. 1825-1833, 1999.
- [20] M. Maeda and H. Miyajima, “Adaptation strength according to neighborhood ranking of self-organizing neural networks,” IEICE Trans. Fundamentals, Vol.E85-A, pp. 2078-2082, 2002.
- [21] N. Shigei, H. Miyajima, and M. Maeda, “Numerical evaluation of incremental vector quantization using stochastic relaxation,” IEICE Trans. Fundamentals, Vol.E87-A, pp. 2364-2371, 2004.
- [22] M. Maeda, N. Shigei, and H. Miyajima, “Adaptive vector quantization with creation and reduction grounded in the equinumber principle,” Journal of Advanced Computational Intelligence and Intelligent Informatics, Vol.9, No.6, pp. 599-606, 2005.
- [23] E. Goles, F. Fogelman, and D. Pellegrin, “Decreasing energy functions as a tool for studying threshold networks,” Discrete Appl. Math., Vol.12, pp. 261-277, 1985.
- [24] H. Miyajima, S. Yatsuki, and M. Maeda, “Some characteristics of higher order neural networks with decreasing energy functions,” IEICE Trans. Fundamentals, Vol.E79-A, pp. 1624-1629, 1996.
- [25] C.-H. Wu, R. E. Hodges, and C.-J. Wang, “Parallelizing the selforganizing feature map on multiprocessor systems,” Parallel Comput., Vol.17, pp. 821-832, 1991.
- [26] K. K. Parhi, F. H. Wu, and K. Genesan, “Sequential and parallel neural network vector quantizers,” IEEE Trans. Comput., Vol.43, pp. 104-109, 1994.
- [27] K. Sano, S. Momose, H. Takizawa, H. Kobayashi, and T. Nakamura, “Efficient parallel processing of competitive learning algorithm,” Parallel Comput., Vol.30, pp. 1361-1383, 2004.
- [28] T. M. Madhyastha and D. A. Reed, “Learning to classify parallel input/output access patterns,” IEEE Trans. Parallel and Distributed Systems, Vol.13, No.8, pp. 802-813, 2002.
- [29] J. Liu, M. A. Brooke, and K. Hirose, “A CMOS feedforward neuralnetwork chip with on-chip parallel learning for oscillation cancellation,” IEEE Trans. Neural Networks, Vol.13, No.5, pp. 1178-1186, 2002.
- [30] T. Kohonen, “Things you haven’t heard about the self-organizing map,” IEEE Proc. Int. Conf. Neural Networks, pp. 1147-1156, 1993.
- [31] Y. Linde, A. Buzo, and R. M. Gray, “An algorithm for vector quantizer design,” IEEE Trans. Commun., Vol.28, pp. 84-95, 1980.
- [32] H. Ritter, T. Martinetz, and K. Schulten, “Neural computation and self-organizing maps, an introduction,” Addison-Wesley, 1992.

This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.